Vinjeru Trust School Learning together to grow in wisdom Vinjeru Trust School ‘The volume of a fixed mass of gas is inversely proportional to the pressure acting on it at constant temperature.’ 1 𝑉1 × 𝑃1 = 𝑉2 × 𝑃2 𝑉∞ 𝑃 at a fixed temperature. 1 𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑃 𝑉 × 𝑃 = constant A quantity of gas has a volume of 9 dm3 is under a pressure of 150 kPa. The pressure on the gas is increased to 200 kPa while its temperature is kept constant. What is the new volume of the gas? 𝑉1 × 𝑃1 = 𝑉2 × 𝑃2 𝑉1 = 9 dm3 𝑃1 = 150 kPa 9 × 150 = 𝑉2 × 200 𝑉2 = ? 𝑃2 = 200 kPa Learning together to grow in wisdom 𝑽𝟐 = 𝟔. 𝟕𝟓 𝒅𝒎𝟑 Vinjeru Trust School ‘The volume of a fixed mass of gas is directly proportional to its temperature at constant pressure.’ 𝑉∞𝑇 at a fixed pressure. 𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑇 𝑉 = constant 𝑇 𝑉1 𝑉2 = 𝑇1 𝑇2 A quantity of gas has a volume of 9 dm3 and a temperature of 27°C. If the pressure is kept constant and the gas is heated to 52°C, to what volume will it expand? 𝑉1 𝑉2 = 𝑉1 = 9 dm3 𝑇1 𝑇2 𝑇1 = 27 + 273 = 300𝐾 9 𝑉2 = 300 325 𝑉2 = ? 𝑇2 = 52 + 273 = 325𝐾 Learning together to grow in wisdom 𝑽𝟐 = 𝟗. 𝟕𝟓 𝒅𝒎𝟑 Vinjeru Trust School ‘The pressure of a fixed mass of gas is directly proportional to its temperature in Kelvin at constant volume.’ 𝑃∞𝑇 at a fixed pressure. 𝑃 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑇 𝑃 = constant 𝑇 𝑃1 𝑃2 = 𝑇1 𝑇2 A quantity of gas has a pressure of 1 atm and a temperature of 350°C. If the volume is kept constant, determine the pressure if the gas is heated to 450°C. 𝑃1 𝑃2 = 𝑃1 = 1 𝑎𝑡𝑚 𝑇1 𝑇2 𝑇1 = 350 + 273 = 623𝐾 1 𝑃2 = 623 723 𝑃2 = ? 𝑇2 = 450 + 273 = 723𝐾 Learning together to grow in wisdom 𝑷𝟐 = 𝟏. 𝟏𝟔 𝒂𝒕𝒎 Vinjeru Trust School ‘Boyle’s law, Charles’ law and Gay-Lussac’s law can be combined for a fixed mass of gas. This is known as the ideal gas equation. 𝑃∞𝑇 at a fixed pressure. 𝑃𝑉 = constant 𝑇 A gas in a container is at a pressure of 12 atm, a volume of 23 dm3 and a temperature of 200 K. The pressure is increased to 14 atm and the temperature is increased to 300K. What is the new volume of the gas? 𝑃1 = 12 𝑎𝑡𝑚 𝑃1 𝑉1 𝑃2 𝑉2 = 𝑇1 𝑇2 𝑇1 = 200𝐾 𝑉1 = 23 𝑑𝑚3 𝑃2 = 14 𝑎𝑡𝑚 𝑇2 = 300𝐾 𝑉2 =? Learning together to grow in wisdom 𝑃1 𝑉1 𝑃2 𝑉2 = 𝑇1 𝑇2 12 × 23 14 × 𝑉2 = 200 300 𝑽𝟐 = 𝟐𝟗. 𝟓𝟕𝒅𝒎𝟑